Let a-2-2k- and b- Let c- be a vector such that -c-a-3- - a-b-c-3 and the angle between c- and a-b- be 30o- Then a-c- is equal to-

The correct option is B 2 Given that: |(a̅×b̅)×c̅| =3 We can have |a̅×b̅||c̅| #160;sin 30^∘ = 3 #160;Thus we get, |a̅×b̅| #160;|c ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let a⃗=2î+ĵ...

Question

Let $\to a = 2^i +^j - 2^k$ and $\to b =^i +^j$ . Let $\to c$ be a vector such that $| \to c - \to a | = 3$ . $| (\to a \times \to b) \times \to c | = 3$ and the angle between $\to c$ and $\to a \times \to b$ be $30^{o}$ . Then $\to a \cdot \to c$ is equal to.

\frac{25}{8}

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\frac{1}{8}

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Solution

The correct option is B $2$
Given that: $| (¯ a \times ¯ b) \times ¯ c | = 3$
We can have $| ¯ a \times ¯ b | | ¯ c | sin 30^{\circ} = 3$
Thus we get, $| ¯ a \times ¯ b | | ¯ c | = 6$
Now, we can verify that $¯ a \times ¯ b = 2 i - 2 j + k$
Hence, $¯ a \times ¯ b = \sqrt{4 + 4 + 1} = 3$ , $| ¯ c | = 2$
Now, $| ¯ c - ¯ a | = 2$ {From Question}
and $| ¯ c - ¯ a |^{2} = | ¯ c |^{2} + | ¯ a |^{2} - 2 ¯ c \cdot ¯ a = 9$
$= 4 + 9 - 2 ¯ c \cdot ¯ a = 9$
Hence, $2 ¯ a \cdot ¯ c = 4$
$¯ a \cdot ¯ c = 2$

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Similar questions

Q. Let

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Let →a=2^i+^j−2^k and →b=^i+^j. Let →c be a vector such that |→c−→a|=3. |(→a×→b)×→c|=3 and the angle between →c and →a×→b be 30o. Then →a⋅→c is equal to.

Let $\to a = 2^i +^j - 2^k$ and $\to b =^i +^j$ . Let $\to c$ be a vector such that $| \to c - \to a | = 3$ . $| (\to a \times \to b) \times \to c | = 3$ and the angle between $\to c$ and $\to a \times \to b$ be $30^{o}$ . Then $\to a \cdot \to c$ is equal to.